Composable Behavioral Models and Schematic-Based Simulation of Electrokinetic Lab-on-a-Chip Systems

Abstract

This paper presents composable behavioral models and a schematic-based simulation methodology to enable topdown design of electrokinetic (EK) lab-on-a-chip (LoC). Complex EK LoCs are shown to be decomposable into a system of elements with simple geometry and specific function. Parameterized and analytical models are developed to describe the electric and biofluidic behavior within each element. Electric and biofluidic pins at element terminals support the communication between adjacent elements in a simulation schematic. An analog hardware description language implementation of the models is used to simulate LoC subsystems for micromixing and electrophoretic separation. Both direct current (dc) and transient analysis can be performed to capture the influence of system topology, element sizes, material properties, and operational parameters on LoC system performance. Accuracy (relative error generally less than 5%) and speedup (> 100×) of the schematic-based simulation methodology are demonstrated by comparison to experimental measurements and continuum numerical simulation. Index Terms-Behavioral model, dispersion, lab-on-a-chip, micromixing, schematic-based simulation, top-down design.NOMENCLATURE Variables A Maximum concentration of species band. c Concentration of species band. c m Channel width-averaged concentration of species band. c p pth moment of the concentration in a longitudinal filament of the species band. C e Electric conductivity of buffer, S/m. d n Mixing concentration coefficients. d m Mixing concentration coefficients at inlet of converging/diverging mixing intersection. D Molecular diffusivity of species, m 2 /s. E Electric field strength, V/cm. h Depth of microchannels, µm. I Electric current through buffer, A. L Length of microchannels, µm. L det Detector path length, µm.

System-level modeling and simulation of biochemical assays in lab-on-a-chip devices

“…The pressure and velocity fields are coupled using an implicit pressure-based scheme-SIMPLE (semi-implicit method for pressure-linked equations) (Patankar 1980). The distribution of electric potential and currents is computed using Kirchhoff's law (Wang et al 2006b). In both cases, the software library SuperLU (http://crd.lbl.gov/~xiaoye/SuperLU/) is used for matrix inversion (to solve the resulting system of linear equations).…”

“…A brief description of the models that relate the Fourier coefficients d i,n of analyte concentrations at inlets and outlets in these components is given in Appendix A. More details are discussed elsewhere (Wang et al 2005a(Wang et al , 2006b). In addition, chaotic secondary flows in junctions could be induced at high Reynolds number, e.g., Re~100 (Bothe et al 2006).…”

“…The electric field then is given by E ¼ Àr/ ¼ ÀD/=L: Thus, in terms of the buffer's electric conductivity r, the electric resistance R Elec of the channel that relates the potential drop D/ and the electric current I is given by (Wang et al 2006b)…”

“…where g = y/w (0 £ g £ 1) is the normalized crossstream coordinate, d i,n (in) are the nth Fourier cosine series coefficients (Wang et al 2005a(Wang et al , 2006b) of the analyte concentration profile at the channel inlet and are given by…”

“…Denote d i,m (l) and d i,m (r) (m = 0, 1, 2,…) the Fourier coefficients of concentration profiles of the ith analyte at the left and right inlets, respectively. Then Fourier coefficients d i,n (out) (n = 0,1,2,…) at the merger outlet can be obtained as (Wang et al 2005a(Wang et al , 2006b, …”